markblundeberg

BCH floating transactions: SIGHASH_NOINPUT emulation using CHECKDATASIG covenants

A new sighash flag has been proposed (originally for Lightning, now for Eltoo) which redacts information about the spending inputs, most notably their transaction IDs.

This facility is both powerful and dangerous: it means that signatures intended for one transaction can be used on other transactions. It also makes up a very strong increase in the malleability of transactions. SIGHASH_NOINPUT allows for much more flexible off-chain smart contracts than nonmalleable transactions. Note that Eltoo requires SIGHASH_NOINPUT, for instance. It's not clear whether such a dangerous feature will be adopted on BCH any time soon.

In this gist I'm going to explain that CHECKDATASIG covenants let us write smart contracts that emulate SIGHASH_NOINPUT. This capability alone should in principle allow to build Lightning, Eltoo with bilaterally funded smart contracts on BCH (though, with some significant

markblundeberg

Taproot is an interesting technology to enable multiparty privacy on a bitcoin. Currently, there is a problem with multiparty contracts in that they are obvious deviation from the most common script type (P2PKH), which hurts privacy. The script that gets used will typically indicate exactly what kind of protocol was at play. Also complex P2SH scripts take extra resources (transaction size and CPU cycles).

The basic idea with Taproot is that instead of P2SH where a script is committed by a hash, you can hide a script (or set of possible scripts) as a commitment within a normal-looking public key. Now there are two ways to spend from this public key:

1. Create a normal transaction signature using the public key, or,
2. Reveal the commitment, and provide parameters that satisfy the revealed script.

To do #1, it means you need to know the private key, or, you have a set of signers who are able to produce a signature (that's where Schnor

markblundeberg

Progressive knockout block filters

In my last gist, I described how the BIP158 block filters are technically not quite optimal, though in an inconsequential way since the false positive rate has been made so low.

In this document I'm going to describe how it's possible to significantly beat the bandwidth requirements of BIP158 while also achieving a lower overall false positive rate. The idea is to prepare multiple independent filters per block, each of which which has a higher false positive rate. Practically this can give roughly a factor of two improvement over BIP158, but at the cost of additional complexity.

The problem

The BIP158 false positive rate was chosen with a particular size of wallet in mind -- somewhere around 1000 items (addresses) to watch in each block. There is a trade off between the overall size of the filter (which must be do

markblundeberg

Further minimizing the redundancy in Neutrino filters (BIP158 / Golomb sets)

Last year saw the introduction of BIP158 and Neutrino wallet which use Golomb-coded sets to very efficiently encode which items are in bitcoin blocks.

The basic idea in BIP158 is that we have N items of interest (such as distinct scriptPubKeys) in a block, which we hash to integers in the interval [0,F-1] for some range F that is much larger than N. These are basically short hashes, but with an uneven number of bits. This set of hashes can be queried to check whether a candidate scriptPubKey might be in a block, by computing the hash for the candidate and checking if that integer is in the set. The false positive rate is approximately N/F, and can be therefore tuned by making F larger or smaller.

Golomb-Rice comes into play by providing a very size-efficient way of encoding the list of hashes (by sorting them and encoding just the differences with an entropy-optimized code), which is important for minimizing over

markblundeberg

It's quite common to see smart contract constructions like this:

OP_IF
    <clause 1 conditions>
    <pubkey1> OP_CHECKSIG
OP_ELSE
    <clause 2 conditions>
    <pubkey2> OP_CHECKSIG
OP_ENDIF

markblundeberg

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SwapChannels: hide your atomic swaps using ordinary payment channels

Dr. Mark B Lundeberg, 2018 July 13 bitcoincash:qqy9myvyt7qffgye5a2mn2vn8ry95qm6asy40ptgx2

Earlier this year I posted an advisory on a possible attack on certain cross-cryptocurrency atomic swap contracts.

markblundeberg

Using PGP signatures with bitcoin script OP_CHECKDATASIG

Dr. Mark B. Lundeberg, 2018 August 30 bitcoincash:qqy9myvyt7qffgye5a2mn2vn8ry95qm6asy40ptgx2

Since version 2.1, GnuPG is able to use the very same secp256k1 elliptic curve signature algorithm (ECDSA) as used in bitcoin. Quite soon Bitcoin Cash will add a new script opcode OP_CHECKDATASIG that is able to check signatures not just on the containing transaction, but also on arbitrary data. For fun, let's try to intersect the two signature systems and see what can be done!

Background

OP_CHECKDATASIG signatures

markblundeberg

Quadratic sighash remains in Segwitv0/BCH/BSV digest algorithms.

Mark Lundeberg 2018 Oct 17

Abstract: Both BCH post-forkday signatures and the BIP143 Segwit signatures are ostensibly designed to remove the 'quadratic hashing problem', however as I will show, they are still vulnerable for long scripts. Back-of-the-envelope calculations show that it will become a serious concern if the existing script limits are relaxed.

Facts

• Every OP_CHECKSIG requires hashing a potentially large amount of data, limited only by the size of scriptCode. The precise length is 159 + len(scriptCode) for scriptCodes longer than 255 bytes, up to 65535 bytes.
• Since many OP_CHECKSIG calls are possible within a given script, this means transactions can be made where the required hashing time is quadratic in the length of script. (though, see the non-push opcod